Tova trotted towards the hurdle with the single-minded determination of a champion, propelled herself skyward and cleared the dauntingly high fence to applause from the spectators crowding around the straw bale arena.

This was no ordinary dressage, however: Tova was a small lop-eared brown and white bunny from Stockholm and the breakout star of this weekend's London Pet Show.

For the 400 beasts at the Earls Court show, it is no longer enough to bark like a dog or purr like a cat: if they couldn't be miraculously tiny – micropigs, 28-in horses, pygmy hedgehogs – they had to jump, dance, herd ducks or ride skateboards.

A dancing dog may have triumphed in last year's Britain's Got Talent but the bar to being a member of the animal celebrity world is even higher these days, and the rabbits of Sweden – watched by Bruce Forsyth, who knows a thing or two about star quality – cleared it effortlessly.

"In Sweden it's so normal, everyone has done it," said Karin Molin, 25, who has trained showjumping rabbits since she was five. Since this equestrian-style sport took off in country backyards in the early 1980s, kaninhop has spread across Scandinavia to Germany and Switzerland.

While Molin's rabbit, Micro, was panting after clearing hurdles at least five times its height, she said her 18 jumping bunnies lived longer than ordinary pets – up to 12 years old – because they were so fit. Fed ordinary hay, pellets and vegetables, the quality she most prized is speed – after that, the jumping comes naturally. "You can't force them," she said.

We may once have subjected our pets to Victorian-style discipline but the London Pet Show promoted if not spectacular indulgence, then at least a very modern, reward-based approach to pet ownership.

A swedish showjumping bunny at the London Pet Show, at Earls Court. Photograph: Felix Clay for the Guardian

The chickens riding skateboards were the work of animal behaviourist Chirag Patel. In less than an hour on the first morning of the show, Patel taught Mercedes – a diminutive bantam – to recognise the colour red, and repeatedly peck at a red plastic square instead of a green or yellow one.

"In the old days it was thought you had to dominate an animal," said Patel. "Actually, the science says you can motivate the animal. We focus on positive reinforcement and giving the animal a reason to play our silly games."

For Mercedes, that reason was mealworms, her reward when she obeyed Patel's clicker, which is used by dog trainers. In this way, he has trained everything from cheetahs (where training animals to submit to teeth-brushing or blood tests without sedation reduces stress for both animal and zookeeper) to goldfish, which can be taught with a torch. "The five-second memory thing with a goldfish is a myth," said Patel. "Any animal with a nervous system has the ability to learn. If they didn't, they wouldn't survive."

Bling dog collars were out as usual; this year it was all about hypoallegenic nutrition for dogs, "enrichment" – properly stimulating pets – and the scary-sounding Raw, which is actually Rabbit Awareness Week.

If animals were taking human form, then humans were taking animal form, and amid the profusion of people hissing at snakes and squawking at parrots stood overheated humans in animal costumes.

Children with a snake at the London Pet Show. Photograph: Felix Clay/Felix Clay for the Guardian

Sacha Langfield, an account manager, had been talked into wearing an unwieldy cat costume to promote Natural & Clean biodegradable cat litter, made from vegetable waste. "I was a little concerned when I went into the dog area earlier," she said, relieved that at least she did not have to squat in an enormous tray of litter.

The London Pet Show has expanded in each of its three years and exhibitors claim the pet industry is proving remarkably recession-proof.

According to Nick Spellman, a children's entertainer who works with exotic animals, pet businesses have ridden out the downturn because children's passions are the last to be cut from the household budget. "Children are left untouched by recession – it's the grownup perks that tend to go first," he said.

James Derbyshire of Boggio Studios, which specialises in family portraits with pets, also reported downturn-busting business. "People will spend more money on their portraits if their pets are in it than if their children are in it," he said. "A woman rang up last week and spent 10 minutes arranging a portrait with her Staffy. At the end of the conversation she said, 'Oh, can I bring my children too?'.

"That sums it up really. The relationship with your pets is more intense sometimes because they are not with us for so long."

Amid the profusion of chatty owls, well-mannered miniature horses with manes crimped more perfectly than My Little Ponies and bearded dragons positively purring at all the attention, one group stuck stubbornly to their animal nature: every single cat was asleep. And no amount of cajoling could conjure a song or a dance out of them.

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